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It is clear that we are still not in possession of a working theory of jet collimation. I have argued the case that magnetic fields, originating on accretion disks are involved but, as I have also indicated, alternative explanations cannot be excluded. Indeed, the diversity of jet forms may be matched by a similar variety of physical explanations. Further progress requires a combination of observational input and theoretical calculation. Let us take these in turn.

5.1. What Theorists Would Like To Know From Observers

(i) What is the scale of jet collimation? As I have indicated above, there is already observational evidence in the case of both AGN and YSO jets that they do not emerge from their energy sources fully collimated. Instead they seem to have to propagate through gtapprox 100 scalelengths before they satisfy an observer's definition of a jet. Prospects for probing the jet collimation scale using VLBI are good. The combination of the VLBA and European VLBI networks, particularly at high frequency (called the World Array) promises just such information in high dynamic range maps. There have been hints of structure perpendicular to the main jet axes already and it may be just possible to image the accretion flows themselves, perhaps through scattered radiation created by either the induced Compton or the stimulated Raman processes. In the case of the optical jets associated with YSO, the improved infrared resolution possible with large telescopes like the Keck and VLT telescopes may allow us to address the same issue in an environment where we have a more accurate measurement of the radius of the central object.

(ii) Do cataclysmic variables produce jets? So far we can only say that there is weak evidence for bipolar outflows. This may be just a recapitulation of our understanding of YSO. Alternatively, these objects may genuinely be incapable of good collimation. If so, then a ready explanation is that the ltapprox 2 decades of disk radius found in a typical CV may be inadequate for good collimation. This contrasts with perhaps gtapprox 8 decades of radius in an AGN disk. This argument would lead one to expect jets to be associated with black hole and unmagnetized neutron star XRB. If extragalactic experience is any guide, then perhaps the best hope of finding jets is through low frequency radio observations.

(iii) How fast are the outflows in the superluminal jets? It seems generally agreed that jet Lorentz factors at least as large as 10 are necessary to account for the observed expansion speeds and inferred degree of beaming. (It seems quite unlikely that jets have a single expansion speed and far more reasonable that the speed diminishes with cylindrical radius.) Less clear-cut is the interpretation of "intraday" variability which leads to uncorrected brightness temperature estimates of ~ 1018 - 1019 K. Interpreted naively as relativistic beaming of incoherent synchrotron radiation, this implies bulk Lorentz factors as large as ~ 100. This is as large as the random Lorentz factors required to produced self-absorbed synchrotron emission at the inverse Compton-limiting temperature of ~ 1012 K in the comoving frame of the plasma. However, as discussed above, it is hard to see how plasma can move this rapidly through an AGN radiation field unless it is pushed by electromagnetic forces. Alternative explanations of intraday variability, notably refractive scintillation, have been proposed which would obviate this conclusion.

(iv) Is there any sign of rotation in jets and bipolar outflows? This would be a clear indication that mechanical angular momentum is being extracted. Unfortunately, the rotational speeds will diminish inversely with cylindrical radius (and even faster if the proportion of magnetic angular momentum in the flow increases), For a non-relativistic stationary, axisymmetric flow, there is a simple result that the total specific angular momentum is the kinematical angular momentum (r2 Omega) of the intermediate critical point. A high resolution, spectroscopic determination of the velocity gradient across a bipolar outflow, presumably in CO, would be very interesting. Of course, this study could also provide information on radial gradients of the axial velocity. Even more challenging observationally would be to do the same thing for the optical jets using Fabry-Perot imaging.

(v) Can we detect evidence for toroidal magnetic field in jets? Perhaps the most direct evidence would come from Faraday rotation gradients across extragalactic radio jets. To date, searches for this effect have yielded ambiguous results. This may be because there is relatively little thermal plasma associated with the flows and most of the variable rotation measure is associated with the foreground. However a good example, especially if the gradient is reversed in a counter-jet, would be quite compelling.

(vi) What physical features of an AGN determine whether it is radio-loud or radio-quiet? This long-standing problem almost certainly has an observational answer. Candidates include: a dense environment stifling incipient jets, a high accretion rate (relative to the Eddington rate) leading to excessive radiative drag on the outflowing plasma and the spin of the central black hole.

(vii) What is the nature of the interaction between the optical and molecular outflows in YSO? Observation of the fast neutral component may be the key to understanding this problem as it may form a buffer between the other two components. As described in section 4.4, depending upon the disposition of thrust with radius, the molecular flow may be decelerating the ionized gas or, alternatively, the ionized gas may be accelerating the molecular gas.

5.2. What Theorists Ought To Try To Understand

(i) How important are boundary conditions in determining the flow pattern of centrifugally-driven winds? It is clear that analytic (or numerical) self-similar solutions are inadequate as they deny the existence of an inner scale, where most of the energy is released, and an outer scale where the major torque is exerted. Even the theorems alluded to above claiming the inevitability of collimation do not seem to address the influence of the outer boundary condition. At our present stage of understanding, the greatest need would appear to be for simple numerical experiments on quasi-stationary flows without too much input physics.

(ii) Are MHD winds stable? This is an even more challenging problem. Most interest centers around global, non-axisymmetric instabilities, generalizations of the kink instability of a Z-pinch as these would probably be the most destructive. However, it would also be of interest to try to generalize the Balbus-Hawley local instability analysis to the differentially rotating, shear flow characteristic of an MHD wind.

(iii) What is the non-linear development of the Balbus-Hawley instability in accretion disks? Again, this is likely to be a numerical problem, that can perhaps be addressed in a shearing box of side comparable with the disk thickness. The buoyant escape of magnetic flux in the vertical direction must be included and the dependence of the results upon the inevitable numerical viscosity should be ascertained. It may only be a matter of semantics but the relationship of this to standard dynamo theory needs to be understood.

(iv) Are thick disks viable? We know that they are subject to linear instability. However, we do not understand if this evolves into a rapid chaotic inflow, stable "planets" or a quasi-stationary configuration in which the inflow limits the growth of the unstable waves that are ultimately responsible for the transport of angular momentum. If it appears that the flow close to rapidly accreting massive black holes in AGN is generically chaotic, then it is likely that the collimation must be achieved at some distance form the hole or jets are confined to disks that are accreting quite subcritically.

(v) At what radius does the "Bardeen-Petterson Effect" operate? Lense-Thirring precession, a peculiarly relativistic effect causes gas to settle into the equatorial plane defined by a spinning black hole. However, it is not well understood at what radius this will be effective (e.g., Kumar 1990). Other torques may have a similar effect.

(vi) What are the thermal and radiative properties of the outflowing gas in a magnetically-dominated, centrifugally-driven wind? We have discussed above the proposal that AGN broad emission lines be associated with this outflow. It is also possible that much of the infrared, in both AGN and YSO, also come from the wind. The local thermal stability of gas under conditions of magnetic dominance deserves further study.

(vii) Does ambipolar diffusion permit sufficient magnetic flux to accumulate for external magnetic torques to be significant in accretion disks? We have argued that the outer parts of disks in AGN and YSO are predominantly molecular. It is not yet certain that we can use the precepts of MHD as a good approximation. It may be that the heating due to ion-neutral friction is an important source of heating.

Listing these questions is a lot easier than answering them.


I am indebted to the ST ScI for financial assistance to attend this meeting and acknowledge financial support under NASA grant NAGW 2372 and NSF grant AST 89-17765.

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